Question

The manufacturer claims that your new car gets 32 mpg on the highway with the standard deviation 5.5 mpg. You suspect that the mpg is more for your car. The 43 trips on the highway that you took averaged 33.3 mpg and. At the 5% significance level of significance:

-Determine the p - value

-At the 5% significance level, determine if the manufacturer meets their claim. Explain your answer in relation to the context.

Answer 1

Solution :

= 32

= 33.3

s = 5.5

n = 43

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 32

Ha : > 32

Test statistic = t

= ( - ) / s / n

= (33.2 -32) / 5.5 / 43

= 1.431

p(t > 1.431 ) = 1-P (t< 1.431) = 0.0799

P-value = 0.0799

= 0.05  

0.0799 > 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that the manufacturer meets their claim.